Multicanonical Spin Glass Simulations

TL;DR

This paper demonstrates that multicanonical Monte Carlo simulations effectively explore the energy landscape of 2D Edwards-Anderson spin glasses, providing insights into groundstates and reducing ergodicity times.

Contribution

The study introduces the application of multicanonical ensemble methods to 2D spin glasses, improving sampling efficiency and enabling analysis of groundstates and thermodynamic quantities.

Findings

Groundstate sampling allows estimation of independent groundstates.

Ergodicity time scales approximately as V^3 with system size.

Multicanonical ensemble enhances simulation efficiency for spin glasses.

Abstract

We report a Monte Carlo simulation of the $2D$ Edwards-Anderson spin glass model within the recently introduced multicanonical ensemble. Replica on lattices of size $L^2$ up to $L=48$ are investigated. Once a true groundstate is found, we are able to give a lower bound on the number of statistically independent groundstates sampled. Temperature dependence of the energy, entropy and other quantities of interest are easily calculable. In particular we report the groundstate results. Computations involving the spin glass order parameter are more tedious. Our data indicate that the large $L$ increase of the ergodicity time is reduced to an approximately $V^3$ power law. Altogether the results suggest that the multicanonical ensemble improves the situation of simulations for spin glasses and other systems which have to cope with similar problems of conflicting constraints.